Correlation CoefficientCorrelation Coefficient

ELESTA1

Correlation Correlation

Measure of relationship between two variables

Ex. Grades in English tends to be related with Foreign Language

Height and weight

Nature of CorrelationNature of Correlation

Magnitude/direction of the relationship

Strength of the relationshipVariance explainedSignificance of the relationship

Magnitude of the RelationshipMagnitude of the Relationship

Positive relationship – as one variable increases the other variable also increases

Ex. academic grades and intelligenceNegative relationship – as one

variable increases, the other decreases or vice versa

Ex. procrastination and motivationAbsence of relationship between

variables – denoted by .00

Strength of RelationshipStrength of Relationship

A correlation coefficient is computed for a bivariate distribution using a statistical formula

Correlation Coefficient ValueInterpretation

0.80 – 1.00 Very strong relationship

0.6 – 0.79 Strong relationship

0.40 – 0.59 Substantial/marked relationship

0.2 – 0.39 Low relationship

0.00 – 0.19 Negligible relationship

VarianceVariance

How much of Y’s is explained/accounted for by X

Proportion explainedSquare of the correlation coefficient

value

Conditions in interpreting rConditions in interpreting r

Linear regression – the points in a scatterplot should tend to fall along a straight line

The size of the r reflects the amount of variance that can be accounted for by a straight line

Homosedasticity – tendency of the standard deviation (or variances) of the arrays to be equal.

Correlational TechniquesCorrelational Techniques

Pearson Product-Moment correlation – (r) used for interval/ratio sets of variables

Spearman Rank-order correlation – two sets of data are ordinal

Phi coefficient – each of the variables is a dichotomy